Answer:
1±√2=q
or
q=2.41, -0.41
Step-by-step explanation:
we are given the equation q²-2q-1=0, and we want to use the quadratic equation, which is (-b±√(b²-4ac))/2a
a is 1 (there is a 1 in front of q²)
b is -2
c is -1
substitute into the equation:
q=(2±√(4-4*1*-1))/2
solve for the discriminant:
√(4-4(1*-1))
√8
now the equation:
(2±√8)/2=q
simplify:
1±√2=q
or if your application asks for a decimal:
√2≈1.41
so:
1+1.41=2.41=q
or
1-1.41=-0.41=q
Hope this helps!
Given the differential equation
dy/dx = 3xy+y^2 / x^2+xy
i) Show that this equation is homogeneous.
ii) By substituting y =xv, solve this differential equation with initial
condition y(1) = 4.
The given differential equation is shown to be homogeneous, and the solution to the equation with the initial condition y(1) = 4 is :
y = 6x^2 * e^(-x/2) - 2x.
i) To show that the differential equation is homogeneous, we need to verify that it is invariant under the transformation y = ux, where u is a function of x.
Let's substitute y = ux into the given differential equation:
dy/dx = 3xy + y^2 / x^2 + xy
Using the chain rule, we can express dy/dx in terms of u and x:
dy/dx = d(ux)/dx = u + x * du/dx
Substituting this into the differential equation:
u + x * du/dx = 3x(ux) + (ux)^2 / x^2 + x(ux)
Simplifying the equation:
u + x * du/dx = 3u + u^2 / x + u
The equation can be further simplified:
x * du/dx = 2u + u^2 / x
We can see that the resulting equation is independent of x. Hence, the original differential equation is homogeneous.
ii) To solve the homogeneous differential equation, let's substitute y = xv back into the equation:
x * du/dx = 2u + u^2 / x
Multiplying through by x:
x^2 * du/dx = 2xu + u^2
Rearranging the equation:
x^2 * du / (2u + u^2) = dx
We can now integrate both sides:
∫ x^2 * du / (2u + u^2) = ∫ dx
The left-hand side can be further simplified using partial fraction decomposition:
∫ (A/u + B/(u+2)) du = ∫ dx
Solving for A and B, we get:
A = -2, B = 1
Substituting back into the integral:
∫ (-2/u + 1/(u+2)) du = ∫ dx
Simplifying the integral:
-2ln|u| + ln|u+2| = x + C
Now substituting u = y/x:
-2ln|y/x| + ln|(y/x)+2| = x + C
Using properties of logarithms, we can simplify this equation further:
ln((y+2x)/x^2) = -x/2 + C
Taking the exponential of both sides:
(y+2x)/x^2 = e^(-x/2+C)
Simplifying the right-hand side by combining e^C into a constant A:
(y+2x)/x^2 = A * e^(-x/2)
Now, solving for y:
y + 2x = Ax^2 * e^(-x/2)
Finally, rearranging the equation to solve for y:
y = Ax^2 * e^(-x/2) - 2x
Given the initial condition y(1) = 4, we can substitute x = 1 and y = 4 into the equation:
4 = A * e^(-1/2) - 2
Solving for A:
A * e^(-1/2) = 6
A = 6 * e^(1/2)
Substituting the value of A back into the equation, we have:
y = 6x^2 * e^(-x/2) - 2x
So the solution to the differential equation with the initial condition y(1) = 4 is y = 6x^2 * e^(-x/2) - 2x.
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Which graph represents an equation with the values shown in the table?
Answer:
4
Step-by-step explanation:
Tommy is helping his mom at the grocery store. He notices that 5 pounds of potatoes cost $2.25. How much would 7 pounds of potatoes cost?
A. $3.45
B. $0.45
C. $3.15
D. $1.61
Answer:
Cost of 7 pound potato = $3.15
Step-by-step explanation:
Given:
Cost of 5 pound potato = $2.25
Find:
Cost of 7 pound potato
Computation:
Cost of 1 pound potato = 2.25 / 5
Cost of 1 pound potato = $0.45
Cost of 7 pound potato = 7 x Cost of 1 pound potato
Cost of 7 pound potato = 7 x 0.45
Cost of 7 pound potato = $3.15
When h is 1/2 and j is 1/3,g is 4. If g varies jointly with h and j, what is the value of g when h is 2 and j is 3?
Answer:
The value of g is 144 when h is 2 and j is 3 .
Step-by-step explanation:
If g varies jointly with h and j.
g = khj
Where k is the constant of proportionality.
Put value in the above
k = 4 × 6
k = 24
As when h = 2 , j = 3 and k = 24 .
Put in the above
g = 2 × 3 × 24
g = 144
Therefore the value of g is 144 when h is 2 and j is 3 .
Shoulda let me have you i coulda made you so happy but ion do 2nd chances, forever i wish u happiness PERIODT DOE.
now its time to make bankk
Answer:
periodttt. get out ya bag n make det money up.
Step-by-step explanation:
brainliestt:)?
PLSS HELPP Find the equation of the line below. If necessary, use a slash (1) to indicate a
division bar.
(6,1)
Answer: 3, -2
Step-by-step explanation: Just divide 6,1 i guess
use the linspace and plot commands in matlab to generate a figure containing the curves y=1.5sin(x) and y=x between x=0 and x=2.5
To generate a figure containing the curves y = 1.5*sin(x) and y = x in MATLAB using the linspace and plot commands, you can follow the steps below:
matlab
% Set the range of x values
x = linspace(0, 2.5, 100);
% Calculate y values for each curve
y1 = 1.5*sin(x);
y2 = x;
% Plot the curves
plot(x, y1, 'b', x, y2, 'r')
% Add labels and title
xlabel('x')
ylabel('y')
title('Curves: y = 1.5*sin(x) and y = x')
% Add a legend
legend('y = 1.5*sin(x)', 'y = x')
% Display the grid
grid on
In this code, we use linspace to create a range of x values from 0 to 2.5 with 100 points. Then, we calculate the corresponding y values for each curve using the equations y1 = 1.5*sin(x) and y2 = x. We use the plot command to plot the curves, with 'b' and 'r' specifying the colors of the curves. Next, we add labels, title, and a legend to the graph. Finally, we display the grid.
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Please help me I only need d.
Answer:
true
Step-by-step explanation:
A group of researchers is designing an experiment to test whether working late at night reduces a person's productivity. The researchers selected a sample of 60 adults, and over the next month, 30 of them will complete assigned tasks late at night whereas the remaining 30 will complete the same tasks during the afternoon. At the end of the month, the researchers will compare the average amount of time it takes each group to complete the tasks. Why is it important that the researchers use randomization to assign each of the adults to a group
Answer: Randomization prevents the researchers from specifically assigning all adults who regularly stay up late to complete assigned tasks late at night.
-Randomization ensures each group will be similar in everything except the time of day they are assigned to work.
-Randomization prevents the adults from selecting their own group.
Step-by-step explanation:
The options include:
a. Randomization ensures each group will be similar in everything except the time of day they are assigned to work.
b. Randomization prevents the adults from selecting their own group.
c. Randomization eliminates lurking variable from the experiment.
d. Randomization prevents the researchers from specifically assigning all adults who regularly stay up late to complete assigned tasks late at night.
e. Randomization ensures that there'll be an equal number of adults in each group.
Randomization refers to a method that is based on chance alone whereby the participants in a particular study are assigned to treatment group. Based on the information given, it us important that the researchers use randomization to assign each of the adults to a group because:
• Randomization ensures each group will be similar in everything except the time of day they are assigned to work.
• Randomization prevents the researchers from specifically assigning all adults who regularly stay up late to complete assigned tasks late at night.
• Randomization prevents the adults from selecting their own group.
What is the solution to the equation?
O
a+5=9
a+53 -9
a+52 +53-9-5
a=3
a+
a+53-9
O a+52 +53 - 9+53
-
a+53-9
3
|
a = 14 3
6
2
Answer:
The format of this equation is wrong
A convex polyhedron has 18 edges and 4 more vertices than faces. How many faces does the polyhedron have?
Answer:
its 22 a yusd the cauculader on mi iPhone ll pro max luser b an f
Answer:
The polyhedron has 8 faces
Step-by-step explanation:
I got it right on the quiz
edge 2021
The heights of adults who identify as men in the U.S. are normally distributed, with a mean of 69.2 inches and a standard deviation of 2.63 inches. The heights of adults who identify as women in the U.S. are also normally distributed, but with a mean of 64.6 inches and a standard deviation of 2.53 inches.
a) If a person who identifies as a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?
z =
b) If a person who identifies as a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?
z =
(a) If a person who identifies as a man is 6 feet 3 inches tall, his z-score will be 2.96.
(b) If a person who identifies as a woman is 5 feet 11 inches tall, her z-score will be 2.17.
(a) To find the z-score, if a person who identifies as a man is 6 feet 3 inches tall.
Explanation: First, convert 6 feet 3 inches to inches.
6 feet 3 inches = (6 x 12) + 3 inches
= 72 + 3 inches
= 75 inches
The formula for calculating the z-score is: z = (x - μ) / σ, where x is the given value, μ is the mean, and σ is the standard deviation.
Substitute the given values in the above formula.
z = (75 - 69.2) / 2.63
= 2.21 / 2.63
= 0.8382
≈ 2.96 (to two decimal places)
(b) To find the z-score, if a person who identifies as a woman is 5 feet 11 inches tall..
Explanation: First, convert 5 feet 11 inches to inches.
5 feet 11 inches = (5 x 12) + 11 inches
= 60 + 11 inches
= 71 inches
The formula for calculating the z-score is: z = (x - μ) / σ, where x is the given value, μ is the mean, and σ is the standard deviation.
Substitute the given values in the above formula.
z = (71 - 64.6) / 2.53
= 6.4 / 2.53
= 2.5336
≈ 2.17 (to two decimal places)
Therefore, the z-score for the given heights of men and women in the US are 2.96 and 2.17 respectively.
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Miguel wants to estimate the average price of a book at a bookstore. The bookstore has 13,000 titles, but Miguel only needs a sample of 200 books. How could Miguel collect a sample of books that is:
cluster sample?
multistage sample?
oversamples?
To best collect a sample of books from the 13,000 titles at the bookstore, Miguel should use a cluster sampling method.
What is the best sampling method?The best sampling method Miguel should use is a cluster sample.
A cluster sample involves dividing the population into clusters or groups and randomly selecting entire clusters to include in the sample.
In this situation, Miguel could divide the bookstore's titles into clusters, such as by genre or shelf location, and randomly select clusters to sample books from.
his method would help ensure representation from different areas of the bookstore and provide a diverse sample of books.
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Find the center of the ellipse.
x2 + 4y2 – 10x – 40y + 121 = 0
Answer:
i dont what an ellipse is but here's the answer:
8x + 32y = 121
Answer:
123‐10×40y=0
10×+40y=123
If you move a decimal to the left 3 times will the numbers increase in value
Answer:
The number will decrease in value
Step-by-step explanation: For example if we had 638.23 if I move the decimal to the left 3 times it would be .63823, and if we add zeros it would look like this, 0.63823 so the number would decrease in value
What is the rate of change of the function described in
the table?
A. 12/5
B. 5
C. 25/2
D. 25
Answer:
B. 5
Step-by-step explanation:
This table does not describe a linear relationship. This is because the table does not have a constant rate of change; between the first two points, the function changes by
(1/2 - 1/10)/(0--1) = (5/10 - 1/10)/(1) = 5/10 - 1/10 = 4/10 = 2/5
Between the second two points, the function changes by
(5/2-1/2)/(1-0) = (4/2)/1 = 4/2 = 2
Comparing the first two y-coordinates, we have 1/10 and 1/2 = 5/10. This is the result of multiplication by 5.
Comparing the second two y-coordinates, we have 1/2 and 5/2. This is the result of multiplication by 5.
Comparing the rest of the y-coordinates, we can see that each time, the y-coordinate is multiplied by 5. This means the rate of change is 5.
Marie's dad drives an SUV that uses 2.5 litres of fuel for every 20 km driven. He drives to work 20 km each way, 5 days a week. How much fuel does he use to get to work every week?
Answer: 12.5 litres
Step-by-step explanation:
The SUV takes 2.5 litres for every 20 km driven.
The trip to work is 20 km which means that going to work costs Marie's father 2.5 litres every day in fuel.
In a week, there are 5 working days.
The amount of fuel used per week is therefore:
= 2.5 * 5
= 12.5 litres
PLEASE HELP I HAVE TO TURN THIS IN IN 1 HOUR!
A round clock on a classroom wall has a diameter of 12 inches. What is the approximate area of the clock?
A. 38 square inches
B. 113 square inches
C. 226 square inches
D. 452 square inches
NO SPAMMING OR LINKS THEY WILL BE REPORTED!
Need Help On This Question!
Answer:
Just multiply the exponents of the numbers
So this is the order from top to below and I'll mark as 1 to 5
2
1
4
5
3
In which interval is the radical function f of x is equal to the square root of the quantity x squared plus 2 times x minus 15 end quantity increasing?
[3, [infinity])
(4, [infinity])
[–5, 3]
(–[infinity], –5] ∪ [3, [infinity])
The correct answer is, [–5, 3]. In the other words, the interval in which the function [tex]f(x) = \sqrt{x^2 + 2x - 15}[/tex] is increasing is [–5, 3].
To determine the interval in which the radical function [tex]f(x) = \sqrt{x^2 + 2x - 15}[/tex] is increasing, we need to find the interval(s) where the derivative of the function is positive.
Let's first find the derivative of f(x):
[tex]f'(x) = (1/2) * (x^2 + 2x - 15)^(-1/2) * (2x + 2)[/tex]
To find where f'(x) > 0, we set f'(x) = 0 and solve for x:
[tex](1/2) * (x^2 + 2x - 15)^(-1/2) * (2x + 2) = 0[/tex]
Since the derivative is never equal to zero (since the denominator (x^2 + 2x - 15)^(-1/2) is never equal to zero), there are no critical points.
To determine the intervals of increase, we can evaluate f'(x) at test points in each interval. We'll consider the intervals defined by the given answer choices:
[3, ∞):
Choose a test point x > 3, let's say x = 4.
Evaluate [tex]f'(4) = (1/2) * (4^2 + 24 - 15)^{(-1/2)} * (24 + 2)[/tex]
[tex]= (1/2) * (16 + 8 - 15)^{(-1/2)} * 10[/tex]
[tex]= (1/2) * (9)^{(-1/2)} * 10[/tex]
= (1/2) * (1/3) * 10
= 5/3
Since f'(4) > 0, the function is increasing in the interval [3, ∞).
(4, ∞):
Choose a test point x > 4, let's say x = 5.
Evaluate f'(5) = (1/2) * (5^2 + 25 - 15)^(-1/2) * (25 + 2)
= (1/2) * (25 + 10 - 15)^(-1/2) * 12
= (1/2) * (20)^(-1/2) * 12
Since f'(5) = 0, the function is not increasing in the interval (4, ∞).
[–5, 3]:
Choose a test point x in the interval, let's say x = 0.
Evaluate [tex]f'(0) = (1/2) * (0^2 + 20 - 15)^{(-1/2)} * (20 + 2)[/tex]
[tex]= (1/2) * (-15)^{-1/2} * 2[/tex]
[tex]= (1/2) * (1/\sqrt{15}) * 2[/tex]
[tex]= 1/\sqrt{15}[/tex]
Since f'(0) > 0, the function is increasing in the interval [–5, 3].
(–∞, –5] ∪ [3, ∞):
Since we have already determined the function is increasing in [–5, 3] and [3, ∞), this interval is valid.
Therefore, the correct answer is, [–5, 3]. In the other words, the interval in which the function [tex]f(x) = \sqrt{x^2 + 2x - 15}[/tex] is increasing is [–5, 3].
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10. Show how to multiply 4/5 by 1/3 using the rectangular model.
To multiply 4/5 by 1/3 using the rectangular model, follow the given steps below:
Step 1: Draw a rectangle and divide it into equal parts (columns and rows) based on the denominator of the given fractions. Here, 5 parts in a row (horizontally) and 3 parts in a column (vertically).
Step 2: Shade in the portion of the rectangle that corresponds to 4/5.
Step 3: Shade in the portion of the rectangle that corresponds to 1/3. You can do this by dividing the height into three equal parts and shading the top part of the rectangle.
Step 4: Find the area of the shaded region of the rectangle. The area of the shaded region of the rectangle is the product of the fractions 4/5 and 1/3. In other words, it is the product of the number of shaded squares in both the shaded regions.
Step 5: Simplify the answer. In this case, you should simplify the product 4/5 × 1/3 before finding the answer. The rectangular model of 4/5 by 1/3 is shown below:
Given fractions: 4/5 and 1/3To find: Multiplication of 4/5 and 1/3 using the rectangular model. The rectangular model is one of the methods to find the multiplication of two fractions visually.
By using this method, we can multiply two fractions by drawing a rectangle that is divided into equal parts based on the denominators of the given fractions and shade in the required portions of the rectangle.
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HELP ASAP SKAKSKKAMAAAAA
Answer:
(240,20)
Step-by-step explanation:
Under her cell phone plan, Lily pays a flat cost of $40 per month and $4 per gigabyte.
She wants to keep her bill under $60 per month. Write and solve an inequality which
can be used to determine x, the number of gigabytes Lily can use while staying within
her budget.
Answer:
16
Step-by-step explanation:
60-44
The inequality is $40 + 4x < $60 and she has to spend 5 gigabytes to stay within her budget
Note that:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
The total amount Lily has to spend has to be less than $60
The total amount she can spend can be represented with this equation
Flat cost + variable cost < $60
Flat cost = $40
Variable cost = cost per gigabyte x gigabyte
$4 × x = $4x
$40 + 4x < $60
To solve for x, combine similar terms
$4x < $60 - $40
$4x < $20
x < 5
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Given any two squares, we can construct a square that equals (in area) the sum of the two given squares. Why?
We cannot construct a square that equals the sum of the areas of two given squares. This statement contradicts the mathematical principles and properties of squares and the Pythagorean theorem.
The statement that given any two squares, we can construct a square that equals the sum of the two given squares is actually false. This statement goes against the well-known mathematical concept known as the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This theorem holds true for right-angled triangles, but it does not hold true for squares.
In fact, if we take two squares and try to add their areas together, the result will not be a square with an area equal to the sum of the two given squares. The resulting shape will be a non-square rectangle or some other irregular shape.
Therefore, we cannot construct a square that equals the sum of the areas of two given squares. This statement contradicts the mathematical principles and properties of squares and the Pythagorean theorem.
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Find the area to the following figure. Round to the one decimal place.
Answer:
91in^2
Step-by-step explanation:
First, add 11 and 15: 11 + 15 = 26
Second, divide it by 2: 26/2 = 13
Third, multiply it by the height: 13 * 7 = 91in^2
4*10^(-3x)=18 Express the solution as a logarithm in base-101010.
Answer:
Hi how are you doing today Jasmine
Answer:
x= -1/3•log10(9/2)
x= -0.218
not sure what the answer is
Given:
Base dimensions of a rectangular prism = 15 cm × x cm
The height of the prism = 8 cm
Volume of the prism = 600 cm.
To find:
The value of x.
Solution:
Base area of the prism is:
[tex]B=length\times width[/tex]
[tex]B=15\times x[/tex]
[tex]B=15x[/tex]
Volume of the prism is:
[tex]V=Bh[/tex]
Where, B is the base area and h is the height of the prism.
Putting [tex]V=600,B=15x,h=8[/tex], we get
[tex]600=15x\times 8[/tex]
[tex]600=(8)(15)x[/tex]
[tex]\dfrac{600}{(8)(15)}=x[/tex]
Therefore, the correct option is C.
Please help! I need the right answer as soon as possible! PLEASE!
Answer:
Volume of the figure = 68 in.³
Step-by-step explanation:
The figure is composed of a rectangular prism and 2 equal triangular prism
Volume of the figure = volume of rectangular prism + 2(volume of triangular prism)
✔️Volume of triangular prism = L*W*H
L = 14 in.
W = 2 in.
H = 2 in.
Volume = 14*2*2 = 56 in.³
✔️Volume of triangular prism = ½*a*c*h
a = 3 in.
c = 2 in.
h = 2 in.
Volume = ½*3*2*2 = 6 in.³
✅Volume go the figure = 56 + 2(6) = 56 + 12
Volume of the figure = 68 in.³
This part has 3 problems of equal weight. Show all the work to get full credit
1. Consider the fixed-point iteration P_k= g(P_k), where g is continuously differentiable on [a, b].
(a) State conditions under which the iteration will converge to the fixed point p € (a, b) for any p_o in that interval.
(b) x= g(x) for g(x)=1/3x²-2/3x+4/3 has two fixed points: 1 and 4. What is the rate of convergence for x_k sufficiently close to each of these two fixed points?
a) The required conditions are i. g(p) = p for p ∈ [a, b].ii. | g'(p) | < 1 for p ∈ (a, b).
b) |x1 - 1| ≤ a|x0 - 1|² for some a > 0, which implies that the iteration converges quadratically to 1 if x0 is sufficiently close to 1.
1. Consider the fixed-point iteration Pk= g(Pk), where g is continuously differentiable on [a, b].
(a) To converge to the fixed point p ∈ (a, b) for any p0 in that interval, the following conditions are required:
i. g(p) = p for p ∈ [a, b].ii. | g'(p) | < 1 for p ∈ (a, b).
(b) For g(x) = 1/3x²-2/3x+4/3, we have two fixed points: 1 and 4.
Let x be sufficiently close to 1:Then, x₁ = g(x₀) = 1/3x₀²-2/3x₀+4/3.
Since g is twice continuously differentiable on (1, 4), by Taylor’s theorem with the integral form of the remainder, we obtain x₁ - 1 = 1/2g"(c)(x₀ - 1)² ≤ 1/2k(x₀ - 1)², where k = supc∈[1,x] | g"(c) | < ∞.
Therefore, |x₁ - 1| ≤ a|x₀ - 1|² for some a > 0, which implies that the iteration converges quadratically to 1 if x0 is sufficiently close to 1.
Similarly, if x is sufficiently close to 4, the iteration converges quadratically to 4.
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Select the proposition that is a tautology. a. (p ^ q) → p b.(p ∨ q) → p с. (р ^ q) → р d. (p ^ q) → p
The proposition that is a tautology is d. (p ^ q) → p. In a tautology, the truth value of the proposition is always true, regardless of the truth values of its individual components.
To determine if a proposition is a tautology, we can construct a truth table and evaluate all possible combinations of truth values for its variables.
For option d, (p ^ q) → p, we have the following truth table:
p q (p ^ q) (p ^ q) → p
T T T T
T F F T
F T F T
F F F T
The proposition that is a tautology is d. (p ^ q) → p.
In a tautology, the truth value of the proposition is always true, regardless of the truth values of its individual components. To determine if a proposition is a tautology, we can construct a truth table and evaluate all possible combinations of truth values for its variables.
For option d, (p ^ q) → p, we have the following truth table:
p q (p ^ q) (p ^ q) → p
T T T T
T F F T
F T F T
F F F T
As we can see, regardless of the truth values of p and q, the proposition (p ^ q) → p always evaluates to true. Therefore, option d is a tautology.
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